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Method for making 2-electron response reduced density matrices approximately N-representable

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Abstract
In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrodinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it ful-fills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.
Keywords
STRONGLY CORRELATED SYSTEMS, CONFIGURATION-INTERACTION, WAVE-FUNCTIONS, NONORTHOGONAL GEMINALS, RENORMALIZATION-GROUP, QUANTUM-CHEMISTRY, ATOMS, OPTIMIZATION, MOLECULES, ELECTRONS

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Citation

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MLA
Lanssens, Caitlin et al. “Method for Making 2-electron Response Reduced Density Matrices Approximately N-representable.” JOURNAL OF CHEMICAL PHYSICS 148.8 (2018): n. pag. Print.
APA
Lanssens, C., Ayers, P. W., Van Neck, D., De Baerdemacker, S., Gunst, K., & Bultinck, P. (2018). Method for making 2-electron response reduced density matrices approximately N-representable. JOURNAL OF CHEMICAL PHYSICS, 148(8).
Chicago author-date
Lanssens, Caitlin, Paul W Ayers, Dimitri Van Neck, Stijn De Baerdemacker, Klaas Gunst, and Patrick Bultinck. 2018. “Method for Making 2-electron Response Reduced Density Matrices Approximately N-representable.” Journal of Chemical Physics 148 (8).
Chicago author-date (all authors)
Lanssens, Caitlin, Paul W Ayers, Dimitri Van Neck, Stijn De Baerdemacker, Klaas Gunst, and Patrick Bultinck. 2018. “Method for Making 2-electron Response Reduced Density Matrices Approximately N-representable.” Journal of Chemical Physics 148 (8).
Vancouver
1.
Lanssens C, Ayers PW, Van Neck D, De Baerdemacker S, Gunst K, Bultinck P. Method for making 2-electron response reduced density matrices approximately N-representable. JOURNAL OF CHEMICAL PHYSICS. 2018;148(8).
IEEE
[1]
C. Lanssens, P. W. Ayers, D. Van Neck, S. De Baerdemacker, K. Gunst, and P. Bultinck, “Method for making 2-electron response reduced density matrices approximately N-representable,” JOURNAL OF CHEMICAL PHYSICS, vol. 148, no. 8, 2018.
@article{8557681,
  abstract     = {{In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrodinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it ful-fills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.}},
  articleno    = {{084104}},
  author       = {{Lanssens, Caitlin and Ayers, Paul W and Van Neck, Dimitri and De Baerdemacker, Stijn and Gunst, Klaas and Bultinck, Patrick}},
  issn         = {{0021-9606}},
  journal      = {{JOURNAL OF CHEMICAL PHYSICS}},
  keywords     = {{STRONGLY CORRELATED SYSTEMS,CONFIGURATION-INTERACTION,WAVE-FUNCTIONS,NONORTHOGONAL GEMINALS,RENORMALIZATION-GROUP,QUANTUM-CHEMISTRY,ATOMS,OPTIMIZATION,MOLECULES,ELECTRONS}},
  language     = {{eng}},
  number       = {{8}},
  pages        = {{12}},
  title        = {{Method for making 2-electron response reduced density matrices approximately N-representable}},
  url          = {{http://dx.doi.org/10.1063/1.4994618}},
  volume       = {{148}},
  year         = {{2018}},
}

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